高稳快速非线性-线性跟踪微分器设计  

Design of Nonlinear-Linear Tracking Differentiator with High Stability and High Speed

作　　者：赵鹏[1] 姚敏立[1] 陆长捷[1] 胡友涛[1] 

机构地区：[1]第二炮兵工程学院602教研室,西安710025

出　　处：《西安交通大学学报》2011年第8期43-48,共6页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(61074072)

摘　　要：针对典型跟踪微分器函数形式复杂、稳定性差和输出振颤明显的问题,设计了一种改进的高稳定性快速收敛非线性-线性跟踪微分器(MTD).首先通过引入非线性奇指数函数环节和线性函数环节构造MTD的跟踪函数,然后利用李雅普诺夫直接法和系统等价性证明MTD的全局渐近稳定性,最后通过对参数物理意义和参数变化对跟踪输出精度影响的分析得到MTD参数整定规则.跟踪过程中,当状态与平衡点距离较远时,MTD以非线性环节为跟踪函数主体驱动状态向平衡点快速收敛,以提高系统输出的跟踪速度;当状态与平衡点接近时,MTD以线性环节为跟踪函数主体驱动状态平稳逼近平衡点,以抑制系统输出振颤.仿真表明,MTD参数容易整定,与典型跟踪微分器相比,MTD在系统稳定性、收敛速度和输出平稳性方面具有优势,且具有滤波功能.A modified nonlinear-linear tracking differentiator （MTD） with high stability and high speed is proposed to improve the performance of tracking differentiator （TD） with complicated function, poor stability and obvious chatter. A combination of a nonlinear odd exponent function and a linear function are introduced into the MTD as a tracking function, and then the global asymptotic stability of MTD is proved using Lyapunov＇s direct method and the equivalence of systems. The principle of parameter tuning is deduced through analyzing the physical meaning and effects of parameters on accuracy of system outputs. In the signal tracking process, the fast convergence to equilibrium point is mainly achieved by the nonlinear exponent function when the state is far away from the equilibrium point, and the linear function works as a main portion in the convergence to generate the output without chattering when the state is near the equilibrium point. Simulation results show that tuning of MTD parameters are simple, and that the perform- ance of MTD is better than the classical TD in stability, tracking speed, smoothness of outputs and filterine.

关 键 词：跟踪微分器 李雅普诺夫直接法 非线性 滤波 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]